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HAT-ZOH
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A 7x7x7 bandaged to behave very similar to a half turn cube but with a slight difference.

The HAT-ZOH was inspired by the HANZOH Cube, built by Takafumi Haseda in 2007 (see the separate entry) which was a disproportionate half-turning 3x3x3. The external basis for the design of this puzzle is the same (you can see the cuboidal corner pieces, for example) and therefore the inventor chose to derive the name from it. The first part of the name was changed to "HAT" and is actually an acronym - for "Half-Axial-Turning" which describes how the puzzle behaves. The hyphen is simply there to emphasize this fact.
Naming this puzzle was quite frustrating. Originally the inventor wanted to call it the HAT-7 cube due to it being based on a 7x7x7 mechanism, but he felt this was not really lending an accurate description. The puzzle does not have seven functional layers per axis of rotation (only three, in fact) but calling it the HAT-3 cube instead was not properly descriptive either as the puzzle has extra pieces besides those you would find in a 3x3x3 cube. He also had considered other names based on the appearance (such as brick cube, crossroads cube, ladder cube and roadway cube) but most were already taken by previous puzzles or didn't really do the complex nature of the puzzle justice in my eyes. So he settled to HAT-ZOH.

The HAT-ZOH Cube is a disproportionate face-cut half-axial-turning cube. In plain text, this is a shallow-cut face turning cube, with each axis having a different cut depth, where the puzzle is half-turning in the context of an axial turn metric (ATM). With a standard half-turn 3x3x3 cube, all layers independently must turn by an integer multiple of 180 degrees to achieve a legal state, but this puzzle relaxes this rule by a small margin: it simply requires that two opposite outer layers together must achieve a turning sum of an integer multiple of 180 degrees. For instance: a clockwise turn of 90 degrees on the top face, followed by an anticlockwise turn of 270 degrees on the bottom (opposing) face, would be a legal move (+90 + -270 = -180 = (-1)*180 degrees, an integer multiple):
Edge length: 69 mm
Weight: 242 grams

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